Restricted Diffusion in Cellular Media : (1+1)-Dimensional Model

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)1682-1694
Journal / PublicationBulletin of Mathematical Biology
Volume73
Issue number7
Publication statusPublished - Jul 2011

Abstract

We consider the diffusion of molecules in a one-dimensional medium consisting of a large number of cells separated from the extra-cellular space by permeable membranes. The extra-cellular space is completely connected and allows unrestricted diffusion of the molecules. Furthermore, the molecules can diffuse within a given cell, i. e., the intra-cellular space; however, direct diffusion from one cell to another cell cannot occur. There is a movement of molecules across the permeable membranes between the intra- and extra-cellular spaces. Molecules from one cell can cross the permeable membrane into the extra-cellular space, then diffuse through the extra-cellular space, and eventually enter the intra-cellular space of a second cell. Here, we develop a simple set of model equations to describe this phenomenon and obtain the solutions using an eigenfunction expansion. We show that the solutions obtained using this method are particularly convenient for interpreting data from experiments that use techniques from nuclear magnetic resonance imaging. © Society for Mathematical Biology 2010.

Research Area(s)

  • Nuclear magnetic resonance imaging, Restricted diffusion in cellular media with permeable membranes

Citation Format(s)

Restricted Diffusion in Cellular Media: (1+1)-Dimensional Model. / Huang, Huaxiong; Wylie, Jonathan J.; Miura, Robert M.
In: Bulletin of Mathematical Biology, Vol. 73, No. 7, 07.2011, p. 1682-1694.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review